2009÷(2009+2009/2010)+1/2011
=2009÷[2009*(1+1/2010)]+1/2011
=1÷(1+1/2010)+1/2011
=1÷2011/2010+1/2011
=1*2010/2011+1/2011
=2010/2011+1/2011
=1
2009÷(2009+2009/2010)+1/2011
=2009÷[2009*(1+1/2010)]+1/2011
=1÷(1+1/2010)+1/2011
=1÷2011/2010+1/2011
=1*2010/2011+1/2011
=2010/2011+1/2011
=1